{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:FLGDQJQ2CZTABKCIWUDMTIUHUO","short_pith_number":"pith:FLGDQJQ2","schema_version":"1.0","canonical_sha256":"2acc38261a166600a848b506c9a287a3a520e291aa4e308c37cf53ab42d5ed4a","source":{"kind":"arxiv","id":"2002.09694","version":1},"attestation_state":"computed","paper":{"title":"A New Family of Boundary-Domain Integral Equations for the Dirichlet Problem of the Diffusion Equation in Inhomogeneous Media with $H^{-1}(\\Omega)$ Source Term on Lipschitz Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"C.Fresneda-Portillo, Z.W. Woldemicheal","submitted_at":"2020-02-22T12:55:32Z","abstract_excerpt":"The interior Dirichlet boundary value problem for the diffusion equation in non-homogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in (Fresneda-Portillo, 2019) different from (Chkadua et. al 2009). We further extend the results obtained in (Fresneda-Portillo, 2019) for the mixed problem in a smooth domain with $L^{2}(\\Omega)$ right hand side to Lipschitz domains and source term $f$ in the Sobolev space $H^{-1}(\\Omega)$, where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2002.09694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-22T12:55:32Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"42e6e5ce1cdbbb193f5b8307a91a3524856789d7901ac67e348e614a4f7b8bdb","abstract_canon_sha256":"18e18509d6e638082c4ce8e4bd9819be1bd7d39ee8613681f923c6302377a492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:53:08.007675Z","signature_b64":"hMs7lXMPd4Hu+gV5ovZ3w9uZeWbIlGdKuYbv2vuzYSLro8m2G2DUHPV5DxZgMI3XgGrJSlVkNVdxkyHtZSvkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2acc38261a166600a848b506c9a287a3a520e291aa4e308c37cf53ab42d5ed4a","last_reissued_at":"2026-07-05T01:53:08.007215Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:53:08.007215Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Family of Boundary-Domain Integral Equations for the Dirichlet Problem of the Diffusion Equation in Inhomogeneous Media with $H^{-1}(\\Omega)$ Source Term on Lipschitz Domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"C.Fresneda-Portillo, Z.W. Woldemicheal","submitted_at":"2020-02-22T12:55:32Z","abstract_excerpt":"The interior Dirichlet boundary value problem for the diffusion equation in non-homogeneous media is reduced to a system of Boundary-Domain Integral Equations (BDIEs) employing the parametrix obtained in (Fresneda-Portillo, 2019) different from (Chkadua et. al 2009). We further extend the results obtained in (Fresneda-Portillo, 2019) for the mixed problem in a smooth domain with $L^{2}(\\Omega)$ right hand side to Lipschitz domains and source term $f$ in the Sobolev space $H^{-1}(\\Omega)$, where neither the classical nor the canonical co-normal derivatives are well defined. Equivalence between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09694","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.09694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2002.09694","created_at":"2026-07-05T01:53:08.007274+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.09694v1","created_at":"2026-07-05T01:53:08.007274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09694","created_at":"2026-07-05T01:53:08.007274+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLGDQJQ2CZTA","created_at":"2026-07-05T01:53:08.007274+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLGDQJQ2CZTABKCI","created_at":"2026-07-05T01:53:08.007274+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLGDQJQ2","created_at":"2026-07-05T01:53:08.007274+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO","json":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO.json","graph_json":"https://pith.science/api/pith-number/FLGDQJQ2CZTABKCIWUDMTIUHUO/graph.json","events_json":"https://pith.science/api/pith-number/FLGDQJQ2CZTABKCIWUDMTIUHUO/events.json","paper":"https://pith.science/paper/FLGDQJQ2"},"agent_actions":{"view_html":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO","download_json":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO.json","view_paper":"https://pith.science/paper/FLGDQJQ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.09694&json=true","fetch_graph":"https://pith.science/api/pith-number/FLGDQJQ2CZTABKCIWUDMTIUHUO/graph.json","fetch_events":"https://pith.science/api/pith-number/FLGDQJQ2CZTABKCIWUDMTIUHUO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO/action/storage_attestation","attest_author":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO/action/author_attestation","sign_citation":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO/action/citation_signature","submit_replication":"https://pith.science/pith/FLGDQJQ2CZTABKCIWUDMTIUHUO/action/replication_record"}},"created_at":"2026-07-05T01:53:08.007274+00:00","updated_at":"2026-07-05T01:53:08.007274+00:00"}